An LES and RANS Study of the Canonical Shock-Turbulence Interaction

Citation

Braun, Noah Oakley (2018) An LES and RANS Study of the Canonical Shock-Turbulence Interaction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/BGX1-C128. https://resolver.caltech.edu/CaltechTHESIS:05212018-165403115

Abstract

The canonical problem of a nearly stationary, nearly planar shockwave passing through isotropic turbulence is investigated within high Reynolds number regimes. The subject flow contains a wide range of turbulent scales and is addressed in Large Eddy Simulation (LES) to relax the otherwise prohibitive computational cost of simulating these flows. Aliasing errors in the LES of the upstream isotropic turbulence are shown to interact with the mean compression of the shock in a problematic matter, and may result in nonphysical behavior such as a reduction in the dissipation rate as the flow crosses the shock. A method for the regularization of LES of shock-turbulence interactions is presented which is constructed to enforce that the energy content in the highest resolved wavenumbers decays as k^-5/3, and is computed locally in physical space at low computational cost. The application of the regularization to an existing subgrid scale model is shown to remove high wavenumber errors while maintaining agreement with DNS of forced and decaying isotropic turbulence. Comparisons to analytical models suggest that the regularization significantly improves the ability of the LES to predict amplifications in subgrid terms over the modeled shockwave.

The regularization method is then employed in high resolution LES intended to illustrate the physical behavior of the shocked, turbulent flow. Turbulent statistics downstream of the interaction are provided for a range of weakly compressible upstream turbulent Mach numbers M_t = 0.03 - 0.18, shock Mach numbers M_s = 1.2 - 3.0, and Taylor-based Reynolds numbers Re_λ = 20 - 2500. The LES displays minimal Reynolds number effects once an inertial range has developed for Re_λ > 100. The inertial range scales of the turbulence are shown to quickly return to isotropy, and downstream of sufficiently strong shocks this process generates a net transfer of energy from transverse into streamwise velocity fluctuations. The streamwise shock displacements are shown to approximately follow a k^-11/3 decay with wavenumber as predicted by linear analysis. In conjunction with other statistics this suggests that the instantaneous interaction of the shock with the upstream turbulence proceeds in an approximately linear manner, but nonlinear effects immediately downstream of the shock significantly modify the flow even at the lowest considered turbulent Mach numbers.

LES allows consideration of high Re_λ flows, but remains expensive to compute relative to lower cost modeling approaches such as Reynolds-Averaged Navier Stokes (RANS). Conventional RANS models are often not well suited for simulations containing discontinuous features such as shocks and, in an effort to improve the performance of RANS, models for averaged shock corrugation effects and the impact of turbulent entropy or acoustic modes on the energy equation are presented. Unlike previous RANS work that has focused on the modification of turbulent statistics by the shock, the proposed models are introduced to capture the effects of the turbulence on the profiles of primitive variables --- mean density, velocity, and pressure. By producing accurate profiles for the primitive variables, it is shown that the proposed models improve numerical convergence behavior with mesh refinement about a shock, and introduce the physical effects of shock asphericity in a converging shock geometry. These effects are achieved by local closures to turbulent statistics in the averaged Navier-Stokes equations, and can be applied in conjunction with existing Reynolds stress closures that have been constructed for broader applications beyond shock-turbulence interactions.

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